the RMS value
How do you give a single size to a wave that is constantly changing, even passing through zero? The RMS value answers a fair question: what steady DC value would heat a resistor just as much? It is the wave's effective, heating-equivalent size.
RMS stands for root-mean-square: square the waveform (making everything positive and weighting big values more), average it, then take the square root. For a sine the result is the peak divided by the square root of 2, about peak times 0.707. So a sine with a 170 V peak has an RMS of about 120 V, which is why a 120 V mains outlet actually peaks near 170 V. Power in a resistor is then simply P = Vrms^2 / R, using RMS just like a DC voltage.
RMS is the honest number for power, heating, and meter readings; a multimeter set to AC reports RMS. Honest caveats: RMS is not the average (a sine's average is zero) and not the peak. Also, the peak-equals-RMS-times-1.414 rule holds only for a pure sine. For a square wave RMS equals the peak, and many cheap meters secretly assume a sine and read wrong on distorted waveforms (a true-RMS meter does not).
A 120 V RMS outlet peaks at 120 times 1.414, about 170 V. A 1500 W heater on it draws Irms = 1500/120 = 12.5 A; you use RMS, not peak, for the power.
RMS is the value that does the heating.
RMS is neither the average nor the peak; and the peak-to-RMS ratio of 1.414 holds only for a sine. Distorted waves break it, and so do non-true-RMS meters.